by Michael O’Farrell
You know the routine. You’re at a carnival. A huckster beckons you into the tent behind his platform. “Ladies. Gentlemen. Step right up. For the meager price of a cup of morning java, just one thin dollar, and we won’t mention just how thin that is these days, Madame Carmen, authentic practitioner of the old world mystic art of divination, will part the veil of eternity and reveal all. Your past. Your present. And. Yes... Your future. Do you dare?” He looks directly at you and, with a wave of his hand, “Step right up...”
You pay the price, mount the creaky wooden stairs and enter the canvas tent through a shimmering of hanging beads. Inside the tent, an old Chovikani sits on a dimly lit stage. In front of her, on a small circular table covered with a tattered cloth adorned with images of the constellations and planets, sits a crystal ball.
“Sit,” she says as she motions you toward the chair opposite of her. She stares into your eyes while passing her hand over the crystal ball. The ball glimmers with an eerie green glow. She peers into the crystal and says, “I see, you are seeking something. Perhaps knowledge of the future, a mate, money.” She gazes at you. Strange, penetrating eyes. “Perhaps, yourself... Closer. I tell you your fortune...”
The crystal ball, the tool of scrying, the eternal trade in desire, is said to reveal all in ghostly images conjured up by the will of the Chovikani. This would imply that every image possible is capable of being viewed in the crystal. Wouldn’t it be nice to own such a crystal ball? Think of the possibilities. Well, “Step right up... Welcome to the digital world.” Technology now adds a new dimension to this trade. We really can have our own personal crystal ball.
The Digital Image
An image is a two-dimensional light “intensity” function, f(x,y) where x and y refer to spatial coordinates and the value of f at the point (x,y) is proportional to the color brightness or gray level. A digital image is an image that has been discretized both in its two-dimensional spatial coordinates and its color and brightness. A digital image is much like a matrix whose row and column indices correlate to a spatial point in the image and the value of matrix at that point is the intensity and color of the digitized image.
A simple method of producing a digital image is with a digital camera. Taking a photograph with a digital camera is similar to taking one with a conventional camera. However, for a digital camera, the image is focused on a charge-coupled device (CCD) or CMOS chip rather than film. The CCD or CMOS is a semiconductor architecture that collects electric charge according to the incident light intensity on its surface, converts that charge to a measurable voltage that is further converted to digital values using an analogue to digital (A/D) converter. These digitized values can be stored in a computer’s digital memory as the digital image.
The digital image is composed of elements called pixels - a contraction of the phrase “picture element.” Each pixel is stored in an array element, the matrix, that quite naturally corresponds to the location of the voltage intensity value on the CCD. The number of pixels of an image is often referred to as the resolution of the image. This is normally written as pair of numbers, 256 x 256 for example, where the first number is the width of the image or the number of horizontal pixels (number of matrix columns), and the second number is the height of the image or the number of vertical pixels (number of matrix rows).
Bits and bytes define the digital world. The word “bit” stands for “binary digit.” A bit has two possible values or states: it is either “on,” in which case its value is one, or it is “off,” and its value is zero. A byte is composed of eight of these zeros and ones comprising a single unit. Since each bit has two possible values, the number of combinations of zeros and ones in a string of bits is a power of 2.
For example, a byte has 8 bits and therefore 28 = 256 possible configurations of zeros and ones. A gray image typically uses one byte to encode a level of gray for a pixel. Therefore each level of gray can be associated with one value from 0 to 255 that can in turn be associated with one unique permutation of eight slots each filled with either a zero or a one.
A typical grayscale uses one byte (8 bits) and encodes a possible 256 discrete levels of gray. The lowest level on the scale, composed of all zeros, is black or zero intensity and the highest level composed of all ones defines the color white or maximum intensity. This same binary structure is used for the each primary color intensity level in a color image.
These numbers are usually written in decimal format instead of binary format where 0 implies none of that primary color is being used and 255 means the full intensity of that color is being used. Each color grayscale is called a channel. There are typically three color channels, one for each of the primary colors: red, green and blue.
With typical gray images there are 28 = 256 possible variations on gray at each pixel location. For each pixel location in a typical color image, there are three possibilities for primary colors (red, green or blue) each with 256 variations of intensity, or 256 x 256 x 256 = 28 x 28 x 28 = 224 possibilities. This is known as 24-bit color.
All 24-bit color digital images can be physically represented given the width, height of the image, i.e. the dimensions of the camera’s sensor. Since these images are actually represented by numeric values, no camera is necessary to realize an image.
Any computer can display an image given only the numbers associated with pixels in the images and the array arrangement of the pixels. In other words, any possible image a digital camera can capture can also be created and displayed using a computer without the use of that camera.
While dealing with large numbers, the number of possibilities for colors for a given number of pixels can also be calculated. Take, for example, 2 pixels. Put one color in one pixel and another, possibly the same, color in the next pixel. Each pixel could have been one of 224 possible colors. So, the number of possible variations for color placement is 224 x 224 = 224*2 variations in the two pixels. Or thought of in another way, there are 248 possible color pictures composed of two pixels.
Now with the same process in mind, consider an 8 x 10-inch picture. We’re talking any picture, which would include all pages of print on an 8.5 x 11-inch paper with half-inch borders. Assume now, that each inch has 600 pixels, then the 8 x 10-inch area will have 8 x 600 = 4800 pixels across and 10 x 600 = 6000 pixels down the page. This gives a total of 28,800,000 pixels on a page.
Now, for those of you who really like large numbers, the number of possible variations for digitized 24-bit color in all of those pixels is a finite number, which is 224*6000*4800 = 224*28,800,000 = 2691,200,000 possible variations for pictures.
The above gargantuan — and that is being kind — number should be realized as the number of possible digital images that can be constructed with 24-bit color and with 600 pixel per inch resolution and of size 8 x 10 inches. And, it is finite. There are not an infinite number of digital images that can be formed with 24-bit color and with 600 pixel per inch resolution and of size 8 x 10 inches. The collection of digital images formed with these variations we’ll label as the Imageverse. It’s certainly not the only such creature, but it is sufficiently large to capture most of the interesting qualities.
Arranging the rows of an image end-to-end and enumerating each pixel in a row by the binary representation of its color, results in a binary number with 24 x 6000 x 4800 digits. A huge number, but just a number and one that is uniquely associated with the image. So the images in the Imageverse can be ordered by the unique number associated with the picture. A number corresponds to a unique image and each image is associated with a unique number. We can count the images. They correspond exactly to the numbers from 0 to 2691,200,000. Nice.
Implications of the Imageverse
The most interesting aspect of the Imageverse, raising the most perplexing questions, is that it is finite in number. This implies that the collection of all color images with 600 pixels per inch resolution that can be placed on an area the size of a standard sheet of paper is finite. Every possible such image from the past, the present, or the future is one of the variations on digital images in the Imageverse. Every imaginable digital image, factual, fictional, or otherwise, happens to be contained in it. If one were to take a camera and go to every possible location in any universe throughout eternity and use any magnification and any orientation, the image snapped would be included the Imageverse. This page itself is in the Imageverse.
So, is this Imageverse real, you ask? Take a look at your TV or your computer screen. Is that image real? You are observing a digital image with probably much less than 6000x4800 screen size, a sub-image of some element of the Imageverse. So is the Imageverse real? It is definitely as real as the Calculus, and for some, far easier to understand, but not as substantial as something made of a more durable material like nylon.
Still, any desired element of the Imageverse can be viewed. Just turn on the TV and feed it the right stuff. It’s always hungry and we like to watch it eat. And, any image from the past present, or future contained in the Imageverse can be viewed at our convenience. Remember, choose a number and get an image or choose an image and get a number.
If we broadcast for eternity, we will assuredly produce an infinite set of images, but how can that be? The Imageverse is finite and only a finite number of its images can be different. This means, in the long, and in this case the very long, run, the same image will be broadcast more often than not. This doesn’t sound too irrational, given the number of reruns on TV today though. And consider also, this is by no means limited to our viewpoint on earth. It includes all images of the same general format, broadcast from alien civilizations in and around Alpha Centauri or anywhere else in the universe. So, if you live longer, get ready for “rerun city.” I’m settled in.
The size of a standard page of paper was chosen for the Imageverse so as to include most books, chart presentations, and scribbled schoolwork. Since words and scribbling can be represented as pictures on a page, every page of printed material that has been, or ever will be, or can be conceptualized in 8 x 10 or smaller format is contained as an image in the Imageverse.
All pages from all books no more than 8 x 10 inches in size are scattered somewhere in there. All the notes scribbled to classmates during all those years in school, including the image of you passing the note to your classmate, are there. Forget the monkeys typing Shakespeare’s plays. Not just books that have been printed, but books that have not yet been printed, books that will never be printed, and books that should never be printed are there.
It is said that the Quran existed before man. Certainly all its pages are contained in the Imageverse and given that the Imageverse exists, it can be concluded therefore that the statement about the Quran is true. The Quran isn’t alone however; there was no time when the Imageverse wasn’t, from a Platonist point of view it has always existed. Recognition of this came with our realization of the digital world. Pages from books have always been there. However, physical instantiation is a different matter.
Patent offices worldwide are head-over-heels trying to put patent information online, i.e. into the Imageverse. Consider however, that all our inventions and discoveries that will ever be made or put in patents are described on 8 x 10 inch page and when put online, will be in the Imageverse. And, if there is a detailed description of any invention or discovery, each page of that presentation is also there.
And — you knew this was coming — there can be only a finite number of such pages. Is there an end to knowledge? Certainly there must be only a finite number of discoveries or inventions that can be noted on a page in some recognizable format. But there might well be knowledge that cannot be passed between us in a format that can be put into the Imageverse. Some variety of knowledge that cannot be visualized in any possible manner of encoding onto a printed page, but is still understood. Pretty strange stuff. Can you imagine what a drop of that would taste like? And, what are the implications of knowing that there are only a finite number of new ideas or inventions that we can communicate between ourselves on a page?
Will our universe last forever? There is no reason to believe that time is finite, although from our perspective entertaining that idea might seem reasonable. If the universe lasts an infinite period of time, at some point in time, all of the possibilities of the Imageverse that will be displayed at some point in time, will in fact be displayed.
From that point in time, since the number of images is finite, only images that have been viewed previously will be viewed. Déjà vu supreme! Is the universe “restarted”? Possibly playing out in a different order? Is it possible that, in the future, everything is actually different but we can’t tell the difference through imagery? Is existence finite or cyclic or can we tell the difference? Does it matter? It would take quite a while to view each image in the Imageverse. At one image per second, it would require on the order of 2691,199,975 years, and anyone thinking of looking at images for that length of time needs more than images in the Imageverse checked.
The Crystal Ball
From our digital world, the television or computer screen can be our crystal ball, a window limited only by our attempts at visualization. There are probably more images in the Imageverse than humans can visually imagine in either the past, the present or the future. All available at your fingertips.
If you need that detailed description on the method of propulsion that powers spaceships between galaxies, how to build the “Ringworld”, the exact values of stocks on the stock market one week from now, or a copy of the best novel ever written, look no further than the crystal ball on your desktop. Can’t go wrong searching in the Imageverse, exactly what you seek is there.
Need that special image as evidence for a court appearance, such as an accident as it happens, a cheating husband caught in the act, or assassination plot in progress? Maybe there is a way to extract your fantasy images, such as those containing images of Abraham Lincoln during his childhood playing with alien children from a neighboring galaxy somewhere in a parallel universe. Where else can you go and expect 100% success — sooner or later, that is.
And, now that we know about the possibilities of the Imageverse, the next step, if it is possible, is find ways to mine useful data from our crystal ball. We could possibly list all of the images of the Imageverse, one by one and evaluate each one for its usefulness.
The staggering size of the Imageverse really presents itself here. Most images have a distinct mirror image and both will be in the Imageverse. If we eliminate mirror images, we reduce the number of images we would have to evaluate by one-half, that’s fifty percent, and a ton of images. This reduction sounds like a lot until you realize that instead of the full 2691,200,000 possibilities to check, there will only be 2691,200,000 /2 possibilities, or written differently, 2691,199,999 possibilities, left to check. We barely dented the surface, a scratch of depth many orders of magnitude less than Planck’s length.
It’s not hard to build a computer program that randomly puts a zero or one in each of 691,200,000 slots. And when we do that, voilà, we have an image. But random images are not often very interesting. They look well scrambled. You might say... random. We definitely need a better way of picking images. We have the crystal ball, we just need the gypsy.
Perhaps some gypsy algorithm that selects only those images you are seeking can be fashioned. Or maybe there is a method of outright selecting images that correspond to an actual physical situation in this universe just like picking apples from a barrel. Who knows? Just remember, if there is a way to mine useful data, the method is detailed in a paper lying somewhere within the depths of the Imageverse. And, as a bonus, a picture of you finding it! Happy hunting.
Copyright © 2014 by Michael O’Farrell